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<a href="_qp_box_linear_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       Quadratic programming solver linear SVM training without bias</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * </span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * </span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * \date        -</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> *</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * </span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * </span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * </span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * </span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> *</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment"> */</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_QP_QPBOXLINEAR_H</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#define SHARK_ALGORITHMS_QP_QPBOXLINEAR_H</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;<a class="code" href="_timer_8h.html">shark/Core/Timer.h</a>&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;<a class="code" href="_quadratic_program_8h.html">shark/Algorithms/QP/QuadraticProgram.h</a>&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;<a class="code" href="_dataset_8h.html">shark/Data/Dataset.h</a>&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;<a class="code" href="_data_view_8h.html">shark/Data/DataView.h</a>&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment"></span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">///</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">/// \brief Quadratic program solver for box-constrained problems with linear kernel</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">///</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">/// \par</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// The QpBoxLinear class is a decomposition-based solver for linear</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// support vector machine classifiers trained with the hinge loss.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// Its optimization is largely based on the paper&lt;br&gt;</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">///   &quot;A Dual Coordinate Descent Method for Large-scale Linear SVM&quot;</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">///   by Hsieh, Chang, and Lin, ICML, 2007.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// However, the present algorithm differs quite a bit, since it</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// learns variable preferences as a replacement for the missing</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">/// working set selection. At the same time, this method replaces</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">/// the shrinking heuristic.</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment">///</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00067" data-start="{" data-end="};">
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html">   67</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_box_linear.html" title="Quadratic program solver for box-constrained problems with linear kernel.">QpBoxLinear</a></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>{</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a5f5ee4e503f9d387f657f41a43297e71">   70</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_box_linear.html#a5f5ee4e503f9d387f657f41a43297e71">DatasetType</a>;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a696d6a324ef267b80dcfa3133a13a341">   71</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="group__shark__globals.html#ga04ea4c6c5368461a8bafa49001695b7d">LabeledData&lt;InputT, unsigned int&gt;::const_element_reference</a> <a class="code hl_typedef" href="classshark_1_1_qp_box_linear.html#a696d6a324ef267b80dcfa3133a13a341">ElementType</a>;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment"></span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">    /// \brief Constructor</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment">    /// \param  dataset  training data</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">    /// \param  dim      problem dimension</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">    ///</span></div>
<div class="foldopen" id="foldopen00079" data-start="{" data-end="}">
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#ad4964a8fe4aaba27dca214bf956ef481">   79</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_box_linear.html#ad4964a8fe4aaba27dca214bf956ef481" title="Constructor.">QpBoxLinear</a>(<span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset, std::size_t dim)</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    : <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>(dataset)</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#acaabcca91e016569f345712678d2aa28" title="input space dimension">m_dim</a>(dim)</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a78c4ce2d9151c4b7014e5850d0125171" title="diagonal entries of the quadratic matrix">m_xSquared</a>(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size())</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size(),0.0)</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#acaabcca91e016569f345712678d2aa28" title="input space dimension">m_dim</a>,0.0)</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size(),1.0)</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>    , <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a285997ddc6b5d29ce7d22dc999032823">m_offset</a>(0)</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(dim &gt; 0);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="comment">// pre-compute squared norms</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size(); i++)</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>        {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="keyword">auto</span> <span class="keyword">const</span>&amp; x_i = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>[i];</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a78c4ce2d9151c4b7014e5850d0125171" title="diagonal entries of the quadratic matrix">m_xSquared</a>(i) = norm_sqr(x_i.input);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        }</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    }</div>
</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    </div>
<div class="foldopen" id="foldopen00099" data-start="{" data-end="}">
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a40ff9688a83628fbb9691f0973ea2e4b">   99</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_box_linear.html#a40ff9688a83628fbb9691f0973ea2e4b">setOffset</a>(<span class="keywordtype">double</span> newOffset){</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a285997ddc6b5d29ce7d22dc999032823">m_offset</a> = newOffset;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>    }</div>
</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    </div>
<div class="foldopen" id="foldopen00103" data-start="{" data-end="}">
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a3dce83db17b67190bd6730e44cdb773e">  103</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_box_linear.html#a3dce83db17b67190bd6730e44cdb773e">offsetGradient</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordtype">double</span> result = 0;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size(); ++i){</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordtype">double</span> y_i = (<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>[i].label &gt; 0) ? +1.0 : -1.0;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>            result += <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>(i) * y_i;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        }</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    }</div>
</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    </div>
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a6db58d9b283d570485001ae03a9b0b87">  112</a></span>    RealVector <span class="keyword">const</span>&amp; <a class="code hl_function" href="classshark_1_1_qp_box_linear.html#a6db58d9b283d570485001ae03a9b0b87">solutionWeightVector</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    }</div>
</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment"></span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span><span class="comment">    /// \brief Solve the SVM training problem.</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span><span class="comment">    /// \param  bound    upper bound for m_alpha-components, complexity parameter of the hinge loss SVM</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span><span class="comment">    /// \param  reg      coefficient of the penalty term \f$-\frac{reg}{2} \cdot \|\m_alpha\|^2\f$, reg=1/C where C is the complexity parameter of the squared hinge loss SVM</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment">    /// \param  stop     stopping condition(s)</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment">    /// \param  prop     solution properties</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">    /// \param  verbose  if true, the solver prints status information and solution statistics</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">    ///</span></div>
<div class="foldopen" id="foldopen00125" data-start="{" data-end="}">
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#ab8274b4499b2b4c342735a3ab338e2fb">  125</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_box_linear.html#ab8274b4499b2b4c342735a3ab338e2fb" title="Solve the SVM training problem.">solve</a>(</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="keywordtype">double</span> bound,</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordtype">double</span> reg,</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <a class="code hl_struct" href="structshark_1_1_qp_stopping_condition.html" title="stopping conditions for quadratic programming">QpStoppingCondition</a>&amp; stop,</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <a class="code hl_struct" href="structshark_1_1_qp_solution_properties.html" title="properties of the solution of a quadratic program">QpSolutionProperties</a>* prop = NULL,</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <span class="keywordtype">bool</span> verbose = <span class="keyword">false</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    ){</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="comment">// sanity checks</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(bound &gt; 0.0);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(reg &gt;= 0.0);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span> </div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="comment">// measure training time</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        <a class="code hl_class" href="classshark_1_1_timer.html" title="Timer abstraction with microsecond resolution.">Timer</a> timer;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="comment">// prepare dimensions and vectors</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        std::size_t ell = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>.size();</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="keywordtype">double</span> prefsum = sum(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>);               <span class="comment">// normalization constant for m_pref</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        std::vector&lt;std::size_t&gt; schedule(ell);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="comment">// prepare counters</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        std::size_t epoch = 0;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        std::size_t steps = 0;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="comment">// prepare performance monitoring for self-adaptation</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordtype">double</span> max_violation = 0.0;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> gain_learning_rate = 1.0 / ell;</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="keywordtype">double</span> average_gain = 0.0;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        <span class="keywordtype">bool</span> canstop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span> </div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        <span class="comment">// outer optimization loop</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>)</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>            <span class="comment">// define schedule</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>            <span class="keywordtype">double</span> psum = prefsum;</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>            prefsum = 0.0;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            std::size_t pos = 0;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>            <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++)</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>            {</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>                <span class="keywordtype">double</span> p = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>[i];</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                <span class="keywordtype">double</span> num = (psum &lt; 1e-6) ? ell - pos : std::min((<span class="keywordtype">double</span>)(ell - pos), (ell - pos) * p / psum);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                std::size_t n = (std::size_t)std::floor(num);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                <span class="keywordtype">double</span> prob = num - n;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>                <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceshark_1_1random.html#ada5e9e6fd77534e1d99479213e5fed50" title="Flips a coin with probability of heads being pHeads by drawing random numbers from rng.">random::coinToss</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>,prob)) n++;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                <span class="keywordflow">for</span> (std::size_t j=0; j&lt;n; j++)</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                {</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                    schedule[pos] = i;</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                    pos++;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                }</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                psum -= p;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                prefsum += p;</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(pos == ell);</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            std::shuffle(schedule.begin(),schedule.end(),<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span> </div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            <span class="comment">// inner loop</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            max_violation = 0.0;</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>            <span class="keywordflow">for</span> (std::size_t j=0; j&lt;ell; j++)</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            {</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>                <span class="comment">// active variable</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>                std::size_t i = schedule[j];</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>                <span class="keyword">auto</span> <span class="keyword">const</span>&amp; e_i = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>[i];</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                <span class="keywordtype">double</span> y_i = (e_i.label &gt; 0) ? +1.0 : -1.0;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span> </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                <span class="comment">// compute gradient and projected gradient</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                <span class="keywordtype">double</span> a = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>(i);</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                <span class="keywordtype">double</span> wyx = y_i * inner_prod(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>, e_i.input);</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                <span class="keywordtype">double</span> g = 1.0 - <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a285997ddc6b5d29ce7d22dc999032823">m_offset</a> * y_i - wyx - reg * a;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                <span class="keywordtype">double</span> pg = (a == 0.0 &amp;&amp; g &lt; 0.0) ? 0.0 : (a == bound &amp;&amp; g &gt; 0.0 ? 0.0 : g);</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span> </div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                <span class="comment">// update maximal KKT violation over the epoch</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>                max_violation = std::max(max_violation, std::abs(pg));</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                <span class="comment">// perform the step</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                <span class="keywordflow">if</span> (pg != 0.0)</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                {</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>                    <span class="comment">// SMO-style coordinate descent step</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                    <span class="keywordtype">double</span> q = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a78c4ce2d9151c4b7014e5850d0125171" title="diagonal entries of the quadratic matrix">m_xSquared</a>(i) + reg;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>                    <span class="keywordtype">double</span> mu = g / q;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                    <span class="keywordtype">double</span> new_a = a + mu;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span> </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                    <span class="comment">// numerically stable update</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                    <span class="keywordflow">if</span> (new_a &lt;= 0.0)</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                    {</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                        mu = -a;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>                        new_a = 0.0;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>                    }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (new_a &gt;= bound)</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                    {</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>                        mu = bound - a;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>                        new_a = bound;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>                    }</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span> </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>                    <span class="comment">// update both representations of the weight vector: m_alpha and m_weights</span></div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                    <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>(i) = new_a;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>                    noalias(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>) += (mu * y_i) * e_i.input;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>                    gain = mu * (g - 0.5 * q * mu);</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span> </div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>                    steps++;</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>                }</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span> </div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>                <span class="comment">// update gain-based preferences</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                {</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>                    <span class="keywordflow">if</span> (epoch == 0) average_gain += gain / (double)ell;</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                    <span class="keywordflow">else</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>                    {</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                        <span class="comment">// strategy constants</span></div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> CHANGE_RATE = 0.2;</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> PREF_MIN = 0.05;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> PREF_MAX = 20.0;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span> </div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                        <span class="keywordtype">double</span> change = CHANGE_RATE * (gain / average_gain - 1.0);</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>                        <span class="keywordtype">double</span> newpref = std::min(PREF_MAX, std::max(PREF_MIN, <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>(i) * std::exp(change)));</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                        prefsum += newpref - <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>(i);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>                        <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>[i] = newpref;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>                        average_gain = (1.0 - gain_learning_rate) * average_gain + gain_learning_rate * gain;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>                    }</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>                }</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>            }</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span> </div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            epoch++;</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>            <span class="comment">// stopping criteria</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            <span class="keywordflow">if</span> (stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#af747ff263a208a610fc2ca4dccec44d6" title="maximum number of decomposition iterations (default to 0 - not used)">maxIterations</a> &gt; 0 &amp;&amp; ell * epoch &gt;= stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#af747ff263a208a610fc2ca4dccec44d6" title="maximum number of decomposition iterations (default to 0 - not used)">maxIterations</a>)</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            {</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>                <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540a1f2d9c58ed6b0985decbfe573d66080d">QpMaxIterationsReached</a>;</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            }</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span> </div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <span class="keywordflow">if</span> (timer.<a class="code hl_function" href="classshark_1_1_timer.html#ad3ccd47c0429d28d9600117b5ed57362" title="Returns the difference between current time and the start time.">stop</a>() &gt;= stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#a2f2037cc62c817ff88ec0801591a0240" title="maximum process time (defaults to 1e100 - not used)">maxSeconds</a>)</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            {</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>                <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540af0f960c500ba6a3c653c9f45efa6e92a">QpTimeout</a>;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            }</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="keywordflow">if</span> (max_violation &lt; stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#addc2ea7f6d15eb25187586e329f33ace" title="minimum accuracy to be achieved, usually KKT violation">minAccuracy</a>)</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                <span class="keywordflow">if</span> (verbose) std::cout &lt;&lt; <span class="stringliteral">&quot;#&quot;</span> &lt;&lt; std::flush;</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>                <span class="keywordflow">if</span> (canstop)</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>                {</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>                    <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540a4b605bae89750d1c2bb1b3ef1a039639">QpAccuracyReached</a>;</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                    <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                }</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>                {</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>                    <span class="comment">// prepare full sweep for a reliable checking of the stopping criterion</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                    canstop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                    <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++) <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>[i] = 1.0;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                    prefsum = (double)ell;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>                }</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>            }</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>            {</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                <span class="keywordflow">if</span> (verbose) std::cout &lt;&lt; <span class="stringliteral">&quot;.&quot;</span> &lt;&lt; std::flush;</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>                canstop = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            }</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        }</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span> </div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        timer.<a class="code hl_function" href="classshark_1_1_timer.html#ad3ccd47c0429d28d9600117b5ed57362" title="Returns the difference between current time and the start time.">stop</a>();</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span> </div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <span class="comment">// compute solution statistics</span></div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        std::size_t free_SV = 0;</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        std::size_t bounded_SV = 0;</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        <span class="keywordtype">double</span> objective = -0.5 * norm_sqr(<a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>);</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++)</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        {</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>            <span class="keywordtype">double</span> a = <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>(i);</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>            <span class="keywordflow">if</span> (a &gt; 0.0)</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            {</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>                objective += a;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>                objective -= reg/2.0 * a * a;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>                <span class="keywordflow">if</span> (a == bound) bounded_SV++;</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>                <span class="keywordflow">else</span> free_SV++;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>            }</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        }</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span> </div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>        <span class="comment">// return solution statistics</span></div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>        <span class="keywordflow">if</span> (prop != NULL)</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>        {</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>            prop-&gt;accuracy = max_violation;       <span class="comment">// this is approximate, but a good guess</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>            prop-&gt;iterations = ell * epoch;</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>            prop-&gt;value = objective;</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>            prop-&gt;seconds = timer.<a class="code hl_function" href="classshark_1_1_timer.html#a91e2a527ffbe3eabc7c8cf36ff742318" title="Returns the last value of stop().">lastLap</a>();</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>        }</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span> </div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        <span class="comment">// output solution statistics</span></div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordflow">if</span> (verbose)</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        {</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            std::cout &lt;&lt; std::endl;</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;training time (seconds): &quot;</span> &lt;&lt; timer.<a class="code hl_function" href="classshark_1_1_timer.html#a91e2a527ffbe3eabc7c8cf36ff742318" title="Returns the last value of stop().">lastLap</a>() &lt;&lt; std::endl;</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of epochs: &quot;</span> &lt;&lt; epoch &lt;&lt; std::endl;</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of iterations: &quot;</span> &lt;&lt; (ell * epoch) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of non-zero steps: &quot;</span> &lt;&lt; steps &lt;&lt; std::endl;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;dual accuracy: &quot;</span> &lt;&lt; max_violation &lt;&lt; std::endl;</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;dual objective value: &quot;</span> &lt;&lt; objective &lt;&lt; std::endl;</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of free support vectors: &quot;</span> &lt;&lt; free_SV &lt;&lt; std::endl;</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of bounded support vectors: &quot;</span> &lt;&lt; bounded_SV &lt;&lt; std::endl;</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        }</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>    }</div>
</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span> </div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba">  326</a></span>    <a class="code hl_class" href="classshark_1_1_data_view.html" title="Constant time Element-Lookup for Datasets.">DataView&lt;const DatasetType&gt;</a> <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a34abab91280fd4241fcd454de20149ba" title="view on training data">m_data</a>;               <span class="comment">///&lt; view on training data</span></div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#acaabcca91e016569f345712678d2aa28">  327</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#acaabcca91e016569f345712678d2aa28" title="input space dimension">m_dim</a>;                                <span class="comment">///&lt; input space dimension</span></div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a78c4ce2d9151c4b7014e5850d0125171">  328</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a78c4ce2d9151c4b7014e5850d0125171" title="diagonal entries of the quadratic matrix">m_xSquared</a>;                            <span class="comment">///&lt; diagonal entries of the quadratic matrix</span></div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232">  329</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#af77735b134d075719f94fe773b3f1232" title="storage of the m_alpha values for warm start">m_alpha</a>;                               <span class="comment">///&lt; storage of the m_alpha values for warm start</span></div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4">  330</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a83c9d19b5cde386a1236928a7ffd94b4" title="storage of weight vector for warm start">m_weights</a>;                                   <span class="comment">///&lt; storage of weight vector for warm start</span></div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488">  331</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a98f0b8dd922bc1abdd26760f9d1de488" title="measure of success of individual steps">m_pref</a>;                <span class="comment">///&lt; measure of success of individual steps</span></div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_box_linear.html#a285997ddc6b5d29ce7d22dc999032823">  332</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classshark_1_1_qp_box_linear.html#a285997ddc6b5d29ce7d22dc999032823">m_offset</a>;</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>};</div>
</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span> </div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span> </div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span><span class="comment">//~ template &lt; &gt;</span></div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span><span class="comment">//~ class QpBoxLinear&lt;CompressedRealVector&gt;</span></div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span><span class="comment">//~ {</span></div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span><span class="comment">//~ public:</span></div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>    <span class="comment">//~ typedef LabeledData&lt;CompressedRealVector, unsigned int&gt; DatasetType;</span></div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span> </div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>    <span class="comment">//~ /// \brief Constructor</span></div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>    <span class="comment">//~ /// \param  dataset  training data</span></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    <span class="comment">//~ /// \param  dim      problem dimension</span></div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>    <span class="comment">//~ QpBoxLinear(const DatasetType&amp; dataset, std::size_t dim)</span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>    <span class="comment">//~ : x(dataset.numberOfElements())</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>    <span class="comment">//~ , y(dataset.numberOfElements())</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>    <span class="comment">//~ , diagonal(dataset.numberOfElements())</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>    <span class="comment">//~ , m_dim(dim)</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <span class="comment">//~ SHARK_ASSERT(dim &gt; 0);</span></div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span> </div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        <span class="comment">//~ // transform ublas sparse vectors into a fast format</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        <span class="comment">//~ // (yes, ublas is slow...), and compute the diagonal</span></div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>        <span class="comment">//~ // elements of the quadratic matrix</span></div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>        <span class="comment">//~ SparseVector sparse;</span></div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>        <span class="comment">//~ for (std::size_t b=0, j=0; b&lt;dataset.numberOfBatches(); b++)</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>            <span class="comment">//~ DatasetType::const_batch_reference batch = dataset.batch(b);</span></div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            <span class="comment">//~ for (std::size_t i=0; i&lt;batch.size(); i++)</span></div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>                <span class="comment">//~ auto const&amp; x_i = shark::get(batch, i).input;</span></div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>                <span class="comment">//~ // if (x_i.nnz() == 0) continue;</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span> </div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>                <span class="comment">//~ unsigned int y_i = shark::get(batch, i).label;</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>                <span class="comment">//~ y[j] = 2.0 * y_i - 1.0;</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>                <span class="comment">//~ double d = 0.0;</span></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>                <span class="comment">//~ for (auto it=x_i.begin(); it != x_i.end(); ++it)</span></div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>                    <span class="comment">//~ double v = *it;</span></div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>                    <span class="comment">//~ sparse.index = it.index();</span></div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>                    <span class="comment">//~ sparse.value = v;</span></div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>                    <span class="comment">//~ storage.push_back(sparse);</span></div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>                    <span class="comment">//~ d += v * v;</span></div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>                <span class="comment">//~ sparse.index = (std::size_t)-1;</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>                <span class="comment">//~ storage.push_back(sparse);</span></div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>                <span class="comment">//~ diagonal(j) = d;</span></div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>                <span class="comment">//~ j++;</span></div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        <span class="comment">//~ for (std::size_t b=0, j=0, k=0; b&lt;dataset.numberOfBatches(); b++)</span></div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>            <span class="comment">//~ DatasetType::const_batch_reference batch = dataset.batch(b);</span></div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>            <span class="comment">//~ for (std::size_t i=0; i&lt;batch.size(); i++)</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>                <span class="comment">//~ auto const&amp; x_i = shark::get(batch, i).input;</span></div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>                <span class="comment">//~ // if (x_i.nnz() == 0) continue;</span></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span> </div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>                <span class="comment">//~ x[j] = &amp;storage[k];   // cannot be done in the first loop because of vector reallocation</span></div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>                <span class="comment">//~ for (; storage[k].index != (std::size_t)-1; k++);</span></div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>                <span class="comment">//~ k++;</span></div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>                <span class="comment">//~ j++;</span></div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span> </div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>    <span class="comment">//~ /// \brief Solve the SVM training problem.</span></div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>    <span class="comment">//~ /// \param  bound    upper bound for m_alpha-components, complexity parameter of the hinge loss SVM</span></div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>    <span class="comment">//~ /// \param  reg      coefficient of the penalty term \f$-\frac{reg}{2} \cdot \|\m_alpha\|^2\f$, reg=1/C where C is the complexity parameter of the squared hinge loss SVM</span></div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>    <span class="comment">//~ /// \param  stop     stopping condition(s)</span></div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>    <span class="comment">//~ /// \param  prop     solution properties</span></div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>    <span class="comment">//~ /// \param  verbose  if true, the solver prints status information and solution statistics</span></div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>    <span class="comment">//~ ///</span></div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>    <span class="comment">//~ RealVector solve(</span></div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>            <span class="comment">//~ double bound,</span></div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>            <span class="comment">//~ double reg,</span></div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>            <span class="comment">//~ QpStoppingCondition&amp; stop,</span></div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>            <span class="comment">//~ QpSolutionProperties* prop = NULL,</span></div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>            <span class="comment">//~ bool verbose = false)</span></div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>        <span class="comment">//~ // sanity checks</span></div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        <span class="comment">//~ SHARK_ASSERT(bound &gt; 0.0);</span></div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>        <span class="comment">//~ SHARK_ASSERT(reg &gt;= 0.0);</span></div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span> </div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <span class="comment">//~ // measure training time</span></div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        <span class="comment">//~ Timer timer;</span></div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>        <span class="comment">//~ timer.start();</span></div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span> </div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>        <span class="comment">//~ // prepare dimensions and vectors</span></div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>        <span class="comment">//~ std::size_t ell = x.size();</span></div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>        <span class="comment">//~ RealVector m_alpha(ell, 0.0);</span></div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>        <span class="comment">//~ RealVector m_weights(m_dim, 0.0);</span></div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        <span class="comment">//~ RealVector m_pref(ell, 1.0);          // measure of success of individual steps</span></div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        <span class="comment">//~ double prefsum = ell;               // normalization constant</span></div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        <span class="comment">//~ std::vector&lt;std::size_t&gt; schedule(ell);</span></div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span> </div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>        <span class="comment">//~ // prepare counters</span></div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span>        <span class="comment">//~ std::size_t epoch = 0;</span></div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span>        <span class="comment">//~ std::size_t steps = 0;</span></div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno">  436</span> </div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>        <span class="comment">//~ // prepare performance monitoring for self-adaptation</span></div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        <span class="comment">//~ double max_violation = 0.0;</span></div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        <span class="comment">//~ const double gain_learning_rate = 1.0 / ell;</span></div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span>        <span class="comment">//~ double average_gain = 0.0;</span></div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        <span class="comment">//~ bool canstop = true;</span></div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span> </div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <span class="comment">//~ // outer optimization loop</span></div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>        <span class="comment">//~ while (true)</span></div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>            <span class="comment">//~ // define schedule</span></div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>            <span class="comment">//~ double psum = prefsum;</span></div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>            <span class="comment">//~ prefsum = 0.0;</span></div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span>            <span class="comment">//~ std::size_t pos = 0;</span></div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>            <span class="comment">//~ for (std::size_t i=0; i&lt;ell; i++)</span></div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>                <span class="comment">//~ double p = m_pref[i];</span></div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>                <span class="comment">//~ double num = (psum &lt; 1e-6) ? ell - pos : std::min((double)(ell - pos), (ell - pos) * p / psum);</span></div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>                <span class="comment">//~ std::size_t n = (std::size_t)std::floor(num);</span></div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>                <span class="comment">//~ double prob = num - n;</span></div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>                <span class="comment">//~ if (random::uni() &lt; prob) n++;</span></div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>                <span class="comment">//~ for (std::size_t j=0; j&lt;n; j++)</span></div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>                    <span class="comment">//~ schedule[pos] = i;</span></div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>                    <span class="comment">//~ pos++;</span></div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>                <span class="comment">//~ psum -= p;</span></div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>                <span class="comment">//~ prefsum += p;</span></div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>            <span class="comment">//~ SHARK_ASSERT(pos == ell);</span></div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>            <span class="comment">//~ for (std::size_t i=0; i&lt;ell; i++) std::swap(schedule[i], schedule[random::discrete(0, ell - 1)]);</span></div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span> </div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>            <span class="comment">//~ // inner loop</span></div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>            <span class="comment">//~ max_violation = 0.0;</span></div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>            <span class="comment">//~ for (std::size_t j=0; j&lt;ell; j++)</span></div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>                <span class="comment">//~ // active variable</span></div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>                <span class="comment">//~ std::size_t i = schedule[j];</span></div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>                <span class="comment">//~ const SparseVector* x_i = x[i];</span></div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span> </div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>                <span class="comment">//~ // compute gradient and projected gradient</span></div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>                <span class="comment">//~ double a = m_alpha(i);</span></div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>                <span class="comment">//~ double wyx = y(i) * inner_prod(m_weights, x_i);</span></div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>                <span class="comment">//~ double g = 1.0 - wyx - reg * a;</span></div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>                <span class="comment">//~ double pg = (a == 0.0 &amp;&amp; g &lt; 0.0) ? 0.0 : (a == bound &amp;&amp; g &gt; 0.0 ? 0.0 : g);</span></div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span> </div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>                <span class="comment">//~ // update maximal KKT violation over the epoch</span></div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>                <span class="comment">//~ max_violation = std::max(max_violation, std::abs(pg));</span></div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span>                <span class="comment">//~ double gain = 0.0;</span></div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span> </div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span>                <span class="comment">//~ // perform the step</span></div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span>                <span class="comment">//~ if (pg != 0.0)</span></div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span>                    <span class="comment">//~ // SMO-style coordinate descent step</span></div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span>                    <span class="comment">//~ double q = diagonal(i) + reg;</span></div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>                    <span class="comment">//~ double mu = g / q;</span></div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>                    <span class="comment">//~ double new_a = a + mu;</span></div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span> </div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>                    <span class="comment">//~ // numerically stable update</span></div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>                    <span class="comment">//~ if (new_a &lt;= 0.0)</span></div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>                    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>                        <span class="comment">//~ mu = -a;</span></div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>                        <span class="comment">//~ new_a = 0.0;</span></div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>                    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>                    <span class="comment">//~ else if (new_a &gt;= bound)</span></div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>                    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span>                        <span class="comment">//~ mu = bound - a;</span></div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span>                        <span class="comment">//~ new_a = bound;</span></div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>                    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span> </div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>                    <span class="comment">//~ // update both representations of the weight vector: m_alpha and m_weights</span></div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>                    <span class="comment">//~ m_alpha(i) = new_a;</span></div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>                    <span class="comment">//~ // m_weights += (mu * y(i)) * x_i;</span></div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>                    <span class="comment">//~ axpy(m_weights, mu * y(i), x_i);</span></div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>                    <span class="comment">//~ gain = mu * (g - 0.5 * q * mu);</span></div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span> </div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>                    <span class="comment">//~ steps++;</span></div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span> </div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span>                <span class="comment">//~ // update gain-based preferences</span></div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>                    <span class="comment">//~ if (epoch == 0) average_gain += gain / (double)ell;</span></div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>                    <span class="comment">//~ else</span></div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>                    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>                        <span class="comment">//~ // strategy constants</span></div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>                        <span class="comment">//~ constexpr double CHANGE_RATE = 0.2;</span></div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>                        <span class="comment">//~ constexpr double PREF_MIN = 0.05;</span></div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>                        <span class="comment">//~ constexpr double PREF_MAX = 20.0;</span></div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span> </div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>                        <span class="comment">//~ double change = CHANGE_RATE * (gain / average_gain - 1.0);</span></div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span>                        <span class="comment">//~ double newpref = std::min(PREF_MAX, std::max(PREF_MIN, m_pref(i) * std::exp(change)));</span></div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>                        <span class="comment">//~ prefsum += newpref - m_pref(i);</span></div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>                        <span class="comment">//~ m_pref[i] = newpref;</span></div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>                        <span class="comment">//~ average_gain = (1.0 - gain_learning_rate) * average_gain + gain_learning_rate * gain;</span></div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno">  530</span>                    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno">  531</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span> </div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span>            <span class="comment">//~ epoch++;</span></div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno">  535</span> </div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span>            <span class="comment">//~ // stopping criteria</span></div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>            <span class="comment">//~ if (stop.maxIterations &gt; 0 &amp;&amp; ell * epoch &gt;= stop.maxIterations)</span></div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>                <span class="comment">//~ if (prop != NULL) prop-&gt;type = QpMaxIterationsReached;</span></div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>                <span class="comment">//~ break;</span></div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span> </div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>            <span class="comment">//~ if (timer.stop() &gt;= stop.maxSeconds)</span></div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>                <span class="comment">//~ if (prop != NULL) prop-&gt;type = QpTimeout;</span></div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno">  546</span>                <span class="comment">//~ break;</span></div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span> </div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>            <span class="comment">//~ if (max_violation &lt; stop.minAccuracy)</span></div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span>                <span class="comment">//~ if (verbose) std::cout &lt;&lt; &quot;#&quot; &lt;&lt; std::flush;</span></div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>                <span class="comment">//~ if (canstop)</span></div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>                    <span class="comment">//~ if (prop != NULL) prop-&gt;type = QpAccuracyReached;</span></div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>                    <span class="comment">//~ break;</span></div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>                <span class="comment">//~ else</span></div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>                <span class="comment">//~ {</span></div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>                    <span class="comment">//~ // prepare full sweep for a reliable checking of the stopping criterion</span></div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>                    <span class="comment">//~ canstop = true;</span></div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>                    <span class="comment">//~ for (std::size_t i=0; i&lt;ell; i++) m_pref[i] = 1.0;</span></div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span>                    <span class="comment">//~ prefsum = ell;</span></div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>                <span class="comment">//~ }</span></div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>            <span class="comment">//~ else</span></div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>                <span class="comment">//~ if (verbose) std::cout &lt;&lt; &quot;.&quot; &lt;&lt; std::flush;</span></div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span>                <span class="comment">//~ canstop = false;</span></div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span> </div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>        <span class="comment">//~ timer.stop();</span></div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span> </div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>        <span class="comment">//~ // compute solution statistics</span></div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>        <span class="comment">//~ std::size_t free_SV = 0;</span></div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>        <span class="comment">//~ std::size_t bounded_SV = 0;</span></div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno">  577</span>        <span class="comment">//~ double objective = -0.5 * shark::blas::inner_prod(m_weights, m_weights);</span></div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno">  578</span>        <span class="comment">//~ for (std::size_t i=0; i&lt;ell; i++)</span></div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno">  580</span>            <span class="comment">//~ double a = m_alpha(i);</span></div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno">  581</span>            <span class="comment">//~ if (a &gt; 0.0)</span></div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno">  582</span>            <span class="comment">//~ {</span></div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno">  583</span>                <span class="comment">//~ objective += a;</span></div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno">  584</span>                <span class="comment">//~ objective -= reg/2.0 * a * a;</span></div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>                <span class="comment">//~ if (a == bound) bounded_SV++;</span></div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno">  586</span>                <span class="comment">//~ else free_SV++;</span></div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno">  587</span>            <span class="comment">//~ }</span></div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno">  588</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno">  589</span> </div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno">  590</span>        <span class="comment">//~ // return solution statistics</span></div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno">  591</span>        <span class="comment">//~ if (prop != NULL)</span></div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>            <span class="comment">//~ prop-&gt;accuracy = max_violation;       // this is approximate, but a good guess</span></div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>            <span class="comment">//~ prop-&gt;iterations = ell * epoch;</span></div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>            <span class="comment">//~ prop-&gt;value = objective;</span></div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>            <span class="comment">//~ prop-&gt;seconds = timer.lastLap();</span></div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span> </div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>        <span class="comment">//~ // output solution statistics</span></div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno">  600</span>        <span class="comment">//~ if (verbose)</span></div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span>            <span class="comment">//~ std::cout &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;training time (seconds): &quot; &lt;&lt; timer.lastLap() &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;number of epochs: &quot; &lt;&lt; epoch &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;number of iterations: &quot; &lt;&lt; (ell * epoch) &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;number of non-zero steps: &quot; &lt;&lt; steps &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;dual accuracy: &quot; &lt;&lt; max_violation &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;dual objective value: &quot; &lt;&lt; objective &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;number of free support vectors: &quot; &lt;&lt; free_SV &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>            <span class="comment">//~ std::cout &lt;&lt; &quot;number of bounded support vectors: &quot; &lt;&lt; bounded_SV &lt;&lt; std::endl;</span></div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span> </div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>        <span class="comment">//~ // return the solution</span></div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno">  614</span>        <span class="comment">//~ return m_weights;</span></div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span>    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span> </div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno">  617</span><span class="comment">//~ protected:</span></div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno">  618</span>    <span class="comment">//~ /// \brief Data structure for sparse vectors.</span></div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>    <span class="comment">//~ struct SparseVector</span></div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span>        <span class="comment">//~ std::size_t index;</span></div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno">  622</span>        <span class="comment">//~ double value;</span></div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno">  623</span>    <span class="comment">//~ };</span></div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span> </div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno">  625</span>    <span class="comment">//~ /// \brief Famous &quot;axpy&quot; product, here adding a multiple of a sparse vector to a dense one.</span></div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno">  626</span>    <span class="comment">//~ static inline void axpy(RealVector&amp; m_weights, double m_alpha, const SparseVector* xi)</span></div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span>    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno">  628</span>        <span class="comment">//~ while (true)</span></div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno">  629</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno">  630</span>            <span class="comment">//~ if (xi-&gt;index == (std::size_t)-1) return;</span></div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno">  631</span>            <span class="comment">//~ m_weights[xi-&gt;index] += m_alpha * xi-&gt;value;</span></div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno">  632</span>            <span class="comment">//~ xi++;</span></div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno">  633</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno">  634</span>    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno">  635</span> </div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno">  636</span>    <span class="comment">//~ /// \brief Inner product between a dense and a sparse vector.</span></div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno">  637</span>    <span class="comment">//~ static inline double inner_prod(RealVector const&amp; m_weights, const SparseVector* xi)</span></div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno">  638</span>    <span class="comment">//~ {</span></div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno">  639</span>        <span class="comment">//~ double ret = 0.0;</span></div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno">  640</span>        <span class="comment">//~ while (true)</span></div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno">  641</span>        <span class="comment">//~ {</span></div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span>            <span class="comment">//~ if (xi-&gt;index == (std::size_t)-1) return ret;</span></div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>            <span class="comment">//~ ret += m_weights[xi-&gt;index] * xi-&gt;value;</span></div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span>            <span class="comment">//~ xi++;</span></div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno">  645</span>        <span class="comment">//~ }</span></div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno">  646</span>    <span class="comment">//~ }</span></div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno">  647</span> </div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno">  648</span>    <span class="comment">//~ std::vector&lt;SparseVector&gt; storage;                ///&lt; storage for sparse vectors</span></div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno">  649</span>    <span class="comment">//~ std::vector&lt;SparseVector*&gt; x;                     ///&lt; sparse vectors</span></div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno">  650</span>    <span class="comment">//~ RealVector y;                                     ///&lt; +1/-1 labels</span></div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno">  651</span>    <span class="comment">//~ RealVector diagonal;                              ///&lt; diagonal entries of the quadratic matrix</span></div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno">  652</span>    <span class="comment">//~ std::size_t m_dim;                                ///&lt; input space dimension</span></div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno">  653</span><span class="comment">//~ };</span></div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno">  654</span> </div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno">  655</span> </div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno">  656</span>}</div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno">  657</span><span class="preprocessor">#endif</span></div>
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